p-Adic physics as a correlate for Boolean cognition

I have had some discussions with Stephen King and Hitoshi Kitada in a closed discussion group about the idea that the duality between Boolean algebras and Stone spaces could be important for the understanding of consciousness, at least cognition. In this vision Boolean algebras would represent conscious mind and Stone spaces would represent the matter: space-time would emerge.

I am personally somewhat skeptic because I see consciousness and matter as totally different levels of existence. Consciousness (and information) is about something, matter just is. Consciousness involves always a change as we no from basic laws about perception. There is of course also the experience of free will and the associated non-determinism. Boolean algebra is a model for logic, not for conscious logical reasoning. There are also many other aspects of consciousness making it very difficult to take this kind of duality seriously.

I am also skeptic about the emergence of space-time say in the extremely foggy form as it used in entropic gravity arguments. Recent day physics poses really strong constraints on our view about space-time and one must take them very seriously.

This does not however mean that Stone spaces could not serve as geometrical correlates for Boolean consciousness. In fact, p-adic integers can be seen as a Stone space naturally assignable to Boolean algebra with infinite number of bits.

1. Innocent questions

I was asked to act as some kind of mathematical consultant and explain what Stone spaces actually are and whether they could have a connection to p-adic numbers. Anyone can of course go to Wikipedia and read the article Stone's representation theorem for Boolean algebras. For a layman this article does not however tell too much.

Intuitively the content of the representation theorem looks rather obvious, at least at the first sight. As a matter fact, the connection looks so obvious that physicists often identify the Boolean algebra and its geometric representation without even realizing that two different things are in question. The subsets of given space- say Euclidian 3-space- with union and intersection as basic algebraic operations and inclusion of sets as ordering relation defined a Boolean algebra for the purposes of physicist. One can assign to each point of space a bit. The points for which the value of bit equals to one define the subset. Union of subsets corresponds to logical OR and intersection to AND. Logical implication B→ A corresponds to A contains B.

When one goes to details problems begin to appear. One would like to have some non-trivial form of continuity.

1. For instance, if the sets are form open sets in real topology their complements representing negations of statements are closed, not open. This breaks the symmetry between statement and it negation unless the topology is such that closed sets are open. Stone's view about Boolean algebra assumes this. This would lead to discrete topology for which all sets would be open sets and one would lose connection with physics where continuity and differential structure are in key role.

2. Could one then dare to disagree with Stone;-) and allow both closed and open sets of E³ in real topology and thus give up clopen assumption? Or could one tolerate the asymmetry between statements and their negations and give some special meaning for open or closet sets- say as kind of axiomatic statements holding true automatically. If so, one an also consider algebraic varieties of lower dimension as collections of bits which are equal to one. In Zariski topology used in algebraic geometry these sets are closed. Again the complements would be open. Could one regard the lower dimensional varieties as identically true statements so that the set of identically true statements would be rather scarce as compared to falsities? If one tolerates some quantum TGD, one could ask whether the 4-D quaternionic/associative varieties defining classical space-times and thus classical physics could be identified as the axiomatic truths. Associativity would be the basic truth inducing the identically true collections of bits.

2. Stone theorem and Stone spaces

For reasons which should be clear it is perhaps a good idea to consider in more detail what Stone duality says. Stone theorem states that Boolean algebras are dual with their Stone spaces. Logic and certain kind of geometry are dual. More precisely, any Boolean algebra is isomorphic to closed open subsets of some Stone space and vice versa. Stone theorem respects category theory. The homomorphisms between Boolean algebras A and B corresponds to homomorphism between Stone spaces S(B) and S(A): one has contravariant functor between categories of Boolean algebras and Stone spaces. In the following set theoretic realization of Boolean algebra provides the intuitive guidelines but one can of course forget the set theoretic picture altogether and consider just abstract Boolean algebra.

1. Stone space is defined as the space of homomorphisms from Boolean algebra to 2-element Boolean algebra. More general spaces are spaces of homomorphisms between two Boolean algebras. The analogy in the category of linear spaces would be the space of linear maps between two linear spaces. Homomorphism is in this case truth preserving map: h(a AND B) = h(a) AND h(B), h(a OR B) = h(a) OR h(B) and so on. These homomorphisms are like always-the-truth-tellers, which are of course social catastrophes;-).

2. For any Boolean algebra Stone space is compact, totally disconnected Hausdorff space. Conversely, for any topological space, the subsets, which are both closed and open define Boolean algebra. Note that for a real line this would give 2-element Boolean algebra. Set is closed and open simultaneously only if its boundary is empty and in p-adic context there are no boundaries. Therefore for p-adic numbers closed sets are open and the sets of p-adic numbers with p-adic norm above some lower bound and having some set of fixed pinary digits define closed-open subsets.

3. Stone space dual to the Boolean algebra does not conform with the physicist's ideas about space-time. Stone space is a compact totally disconnected Hausdorff space. Disconnected space is representable as a union of two or more disjoint open sets. For totally disconnected space this is true for every subset. Path connectedness is stronger notion than connected and says that two points of the space can be always connected by a curve defined as a mapping of real unit interval to the space. Our physical space-time seems to be however connected in real sense.

4. The points of the Stone space S(B) can be identified ultrafilters. Ultrafilter defines homomorphism of B to 2-element of Boolean algebra Boolean algebra. Set theoretic realization allows to understand what this means. Ultrafilter is a set of subsets with the property that intersections belong to it and if set belongs to it also sets containing it belong to it: this corresponds to the fact that set inclusion A ⊃ B corresponds to logical implication. Either set or its complement belongs to ultrafilter (either statement or its negation is true). Empty set does not. Ultrafilter obviously corresponds to a collection of statements which are simultaneously true without contradictions. The sets of ultrafilter correspond to the statements interpreted as collections of bits for which each bit equals to 1.

5. The subsets of B containing a fixed point b of Boolean algebra define an ultrafilter and imbedding of b to the Stone space by assigning to it this particular principal ultrafilter. b represents a statement which is always true, kind of axiom for this principal ultrafilter and ultrafilter is the set of all statements consistent with b.

   Actually any finite set in the Boolean algebra consisting of a collection of fixed bits b_i defines an ultrafilter as the set all subsets of Boolean algebra containing this subset. Therefore the space of all ultra-filters is in one-one correspondence with the space of subsets of Boolean statements. This set corresponds to the set of statements consistent with the truthness of b_i analogous to axioms.

3. 2-adic integers and 2-adic numbers as Stone spaces

I was surprised to find that p-adic numbers are regarded as a totally disconnected space. The intuitive notion of connected is that one can have a continuous curve connecting two points and this is certainly true for p-adic numbers with curve parameter which is p-adic number but not for curves with real parameter which became obvious when I started to work with p-adic numbers and invented the notion of p-adic fractal. In other words, p-adic integers form a continuum in p-adic but not in real sense. This example shows how careful one must be with definitions. In any case, to my opinion the notion of path based on p-adic parameter is much more natural in p-adic case. For given p-adic integers one can find p-adic integers arbitrary near to it since at the limit n→∞ the p-adic norm of pⁿ approaches zero. Note also that most p-adic integers are infinite as real integers.

Disconnectedness in real sense means that 2-adic integers define an excellent candidate for a Stone space and the inverse of the Stone theorem allows indeed to realize this expectation. Also 2-adic numbers define this kind of candidate since 2-adic numbers with norm smaller than 2ⁿ for any n can be mapped to 2-adic integers. One would have union of Boolean algebras labelled by the 2-adic norm of the 2-adic number. p-Adic integers for a general prime p define obviously a generalization of Stone space making sense for effectively p-valued logic: the interpretation of this will be discussed below.

Consider now a Boolean algebra consisting of all possible infinitely long bit sequences. This algebra corresponds naturally to 2-adic integers. The generating Boolean statements correspond to sequences with single non-vanishing bit: by taking the unions of these points one obtains all sets. The natural topology is that for which the lowest bits are the most significant. 2-adic topology realizes this idea since n:th bit has norm 2^-n. 2-adic integers as an p-adic integers are as spaces totally disconnected.

That 2-adic integers and more generally, 2-adic variants of n-dimensional manifolds would define Stone bases assignable to Boolean algebras is consistent with the identification of p-adic space-time sheets as correlates of cognition. Each point of 2-adic space-time sheet would represent 8 bits as a point of 8-D imbedding space. In TGD framework WCW ("world of classical worlds") spinors correspond to Fock space for fermions and fermionic Fock space has natural identification as a Boolean algebra. Fermion present/not present in given mode would correspond to true/false. Spinors decompose to a tensor product of 2-spinors so that the labels for Boolean statements form a Boolean algebra two.

In TGD Universe life and thus cognition reside in the intersection of real and p-adic worlds. Therefore the intersections of real and p-adic partonic 2-surfaces represent the intersection of real and p-adic worlds, those Boolean statements which are expected to be accessible for conscious cognition. They correspond to rational numbers or possibly numbers in n algebraic estension of rationals. For rationals pinary expansion starts to repeat itself so that the number of bits is finite. This intersection is also always discrete and for finite real space-time regions finite so that the identification looks a very natural since our cognitive abilities seem to be rather limited. In TGD inspired physics magnetic bodies are the key players and have much larger size than the biological body so that their intersection with their p-adic counterparts can contain much more bits. This conforms with the interpretation that the evolution of cognition means the emergence of increasingly longer time scales. Dark matter hierarchy realized in terms of hierarchy of Planck constants realizes this.

3. What about p-adic integers with p>2?

The natural generalization of Stone space would be to a geometric counterpart of p-adic logic which I discussed for some years ago. The representation of the statements of p-valued logic as sequences of pinary digits makes the correspondence trivial if one accepts the above represented arguments. The generalization of Stone space would consist of p-adic integers and imbedding of a p-valued Boolean algebra would map the number with only n:th digit equal to 1,...,p-1 to corresponding p-adic number.

One should however understand what p-valued statements mean and why p-adic numbers near powers of 2 are important. What is clear that p-valued logic is too romantic to survive. At least our every-day cognition is firmly anchored to a reality where everything is experience to be true or false.

1. The most natural explanation for p> 2 adic logic is that all Boolean statements do not allow a physical representation and that this forces reduction of 2ⁿ valued logic to p< 2ⁿ valued one. For instance, empty set in the set theoretical representation of Boolean logic has no physical representation. In the same manner, the state containing no fermions fails to represent anything physically. One can represent physically at most 2ⁿ-1 one statements of n-bit Boolean algebra and one must be happy with n-1 completely represented digits. The remaining statements containing at least one non-vanishing digit would have some meaning, perhaps the last digit allowed could serve as a kind of parity check.

2. If this is accepted then p-adic primes near to power 2ⁿ of 2 but below it and larger than the previous power 2^n-1 can be accepted and provide a natural topology for the Boolean statements grouping the binary digits to p-valued digit which represents the allowed statements in 2ⁿ valued Boolean algebra. Bit sequence as a unit would be represented as a sequence of physically realizable bits. This would represent evolution of cognition in which simple yes or not statements are replaced with sequences of this kind of statements just as working computer programs are fused as modules to give larger computer programs. Note that also for computers similar evolution is taking place: the earliest processors used byte length 8 and now 32, 64 and maybe even 128 are used.

3. Mersenne primes M_n=2ⁿ-1 would be ideal for logic purposes and they indeed play a key role in quantum TGD. Mersenne primes define p-adic length scales characterize many elementary particles and also hadron physics. There is also evidence for p-adically scaled up variants of hadron physics (also leptohadron physics allowed by the TGD based notion of color predicting colored excitations of leptons). LHC will certainly show whether M₈₉ hadron physics at TeV energy scale is realized and whether also leptons might have scaled up variants.

4. For instance, M₁₂₇ assignable to electron secondary p-adic time scale is .1 seconds, the fundamental time scale of sensory perception. Thus cognition in .1 second time scale single pinary statement would contain 126 digits as I have proposed in the model of memetic code. Memetic codons would correspond to 126 digit patterns with duration of .1 seconds giving 126 bits of information about percept.

If this picture is correct, the interpretation of p-adic space-time sheets- or rather their intersections with real ones- would represent space-time correlates for Boolean algebra represented at quantum level by fermionic many particle states. In quantum TGD one assigns with these intersections braids- or number theoretic braids- and this would give a connection with topological quantum field theories (TGD can be regarded as almost topological quantum field theory).

4. One more road to TGD

The following arguments suggests one more manner to end up with TGD by requiring that fermionic Fock states identified as a Boolean algebra have their Stone space as space-time correlate required by quantum classical correspondence. Second idea is that space-time surfaces define the collections of binary digits which can be equal to one: kind of eternal truths.In number theoretical vision associativity condition in some sense would define these divine truths. Standard model symmetries are a must- at least as their p-adic variants -and simple arguments forces the completion of discrete lattice counterpart of M⁴ to a continuum.

1. If one wants Poincare symmetries at least in p-adic sense then a 4-D lattice in M⁴ with SL(2,Z)×T⁴, where T⁴ is discrete translation group is a natural choice. SL(2,Z) acts in discrete Minkowski space T⁴ which is lattice. Poincare invariance would be discretized. Angles and relative velocities would be discretized, etc..

2. The p-adic variant of this group is obtained by replacing Z and T⁴ by their p-adic counterparts: in other words Z is replaced with the group Z_pof p-adic integers. This group is p-adically continuous group and acts continuously in T⁴ defining p-adic variant of Minkowski space consisting of all bit sequences consisting of 4-tuples of bits. Only in real sense one would have discreteness: note also that most points would be at infinity in real sense. Therefore it is possible to speak about analytic functions, differential calculus, and to write partial differential equations and to solve them. One can construct group representations and talk about angular momentum, spin and 4-momentum as labels of quantum states.

3. If one wants standard model symmetries p-adically one must replace T⁴ with T⁴ × CP₂. CP₂ would be now discrete version of CP₂ obtained from discrete complex space C³ by identifying points different by a scaling by complex integer. Discrete versions of color and electroweak groups would be obtained.

The next step is to ask what are the laws of physics. TGD fan would answer immediately: they are of course logical statements which can be true identified as subsets of T⁴× CP₂ just as subset in Boolean algebra of sets corresponds to bits which are true.

1. The collections of 8-bit sequences consisting of only 1:s would define define 4-D surfaces in discrete T⁴× CP₂ . Number theoretic vision would suggest that they are quaternionic surfaces so that one associativity be the physical law at geometric level. The conjecture is that preferred extremals of Kähler action are associative surfaces using the definition of associativity as that assignable to a 4-plane defined by modified gamma matrices at given point of space-time surface.

2. Induced gauge field and metric make sense for p-adic integers. p-Adically the field equations for Kähler action make also sense. These p-adic surfaces would represent the analog of Boolean algebra. They would be however something more general than Stone assumes since they are not closed-open in the 8-D p-adic topology.

One however encounters a problem.

1. Although the field equations associated with Kähler action make sense, Kähler action itself does not exists as integral nor does the genuine minimization make sense since p-adically numbers are not well ordered and one cannot in general say which of two numbers is the larger one. This is a real problem and suggests that p-adic field equations are not enough and must be accompanied by real ones. Of course, also the metric properties of p-adic space-time are in complete conflict with what we believe about them. Note however that discretized variants of symmetries might make sense but would reflect finite measurement resolution and cognitive resolution.

2. One could argue that for preferred extremals the integral defining Kähler action is expressible as an integral of 4-form whose value could be well-defined since integrals of forms for closed surface make sense in p-adic cohomology theory pioneered by Grothendieck. The idea would be to use the definition of K\"ahler action making sense for preferred extremals as its definition in p-adic context. I have indeed proposed that space-time surfaces define representatives for homology with inspiration coming from TGD as almost topological QFT. This would give powerful constraints on the theory in accordance with the interpretation as a generalized Bohr orbit.

3. This argument together with what we know about the topology of space-time on basis of everyday experience however more or less forces the conclusion that also real variant of M⁴×CP₂ is there and defines the proper variational principle. The finite points (on real sense) of T⁴× CP₂ (in discrete sense) would represent points common to real and p-adic worlds and the identification in terms of braid points makes sense if one accepts holography and restricts the consideration to partonic 2-surfaces at boundaries of causal diamond. These discrete common would represent the intersection of cognition and matter and living systems and provide a representation for Boolean cognition.

4. Finite measurement resolution enters into the picture naturally. The proper time distance between the tips would be quantized in multiples of CP₂ length. There would be several choices for the discretized imbedding space corresponding to different distance between lattice points: the interpretation is in terms of finite measurement resolution.

It should be added that discretized variant of Minkowski space and its p-adic variant emerge in TGD also in different manner in zero energy ontology.

1. The discrete space SL(2,Z) × T⁴ would have also interpretation as acting in the moduli space for causal diamonds identified as intersections of future and past directed light-cones. T⁴ would represent lattice for possible positions of the lower tip of CD and and SL(2,C) leaving lower tip invariant would act on hyperboloid defined by the position of the upper tip obtained by discrete Lorentz transformations. This leads to cosmological predictions (quantization of red shifts). CP₂ length defines a fundamental time scale and the number theoretically motivated assumption is that the proper time distances between the tips of CDs come as integer multiples of this distance. The stronger condition that they come as octaves of this scale is not in fashion anymore;-).

2. The stronger condition explaining p-adic length scale hypothesis would be that only octaves of the basic scale are allowed. This option is not consistent with zero energy ontology. The reason is that for more general hypothesis the M-matrices of the theory for Kac-Moody type algebra with finite-dimensional Lie algebra replaced with an infinite-dimensional algebra representing hermitian square roots of density matrices and powers of the phase factor replaced with powers of S-matrix. All integer powers must be allowed to obtain generalized Kac-Moody structure, not only those which are powers of 2 and correspond naturally to integer valued proper time distance between the tips of CD. Zero energy states would define the symmetry Lie-algebra of S-matrix with generalized Yangian structure.

3. p-Adic length scale hypothesis would be an outcome of physics and it would not be surprising that primes near power of two are favored because they optimize Boolean cognition.

The outcome is TGD as the skeptical reader already knowing my tricks might have guessed;-). Reader can of course imagine alternatives but remember the potential difficulties due to the fact that minimization in p-adic sense does not make sense and action defined as integral does not exist p-adically. Also the standard model symmetries and quantum classical correspondence are to my opinion "must":s.

5. A connection between cognition, number theory, algebraic geometry, topology, and quantum physics

Stone space is synonym for profinite space. Galois groups associated with algebraic extensions of number fields represent an extremely general class of profinite groups. Every profinite group appears in Galois theory of some field K. The most most interesting ones for algebraic extensions F/K of field K are inverse limits of Gal(F₁/K), where F₁ varies over all intermediate fields. Profinite groups appear also as fundamental groups in algebraic geometry. In algebraic topology fundamental groups are in general not profinite. Profiniteness means that p-adic representations are especially natural for profinite groups.

There is a fascinating connection between infinite primes and algebraic geometry summarized briefly here. This connection lead to the proposal that Galois groups - or rather their projective variants- can be represented as braid groups acting on 2-dimensional surfaces. These findings suggest a deep connection between space-time correlates of Boolean cognition, number theory, algebraic geometry, and quantum physics and TGD based vision about representations of Galois groups as groups lifted to braiding groups acting on the intersection of real and p-adic variants of partonic 2-surface conforms with this.

Fermat theorem serves as a good illustration between the connection between cognitive representations and algebraic geometry. A very general problem of algebraic geometry is to find rational points of an algebraic surface. These can be identified as common rational points of the real and p-adic variant of the surface. The interpretation in terms of consciousness theory would be as points defining cognitive representation as rational points common to real partonic 2-surface and and its p-adic variants. The mapping to polynomials given by their representation in terms of infinite primes to braids of braids of braids.... at partonic 2-surfaces would provide the mapping of n-dimensional problem to a 2-dimensional one (see this).

One considers the question whether there are integer solutions to the equation xⁿ+yⁿ+zⁿ=1. This equation defines 2-surfaces in both real and p-adic spaces. In p-adic context it is easy to construct solutions but they usually represent infinite integers in real sense. Only if the expansion in powers of p contains finite number of powers of p, one obtains real solution as finite integers.

The question is whether there are any real solutions at all. If they exist they correspond to the intersections of the real and p-adic variants of these surfaces. In other words p-adic surface contains cognitively representable points. For n>2 Fermat's theorem says that only single point x=y=z=0 exists so that only single p-adic multi-bit sequence (0,0,0,...) would be cognitively representable.

This relates directly to our mathematical cognition. Linear and quadratic equations we can solve and in these cases the number in the intersection of p-adic and real surfaces is indeed very large. We learn the recipes already in school! For n>2 difficulties begin and there are no general recipes and it requires mathematician to discover the special cases: a direct reflection of the fact that the number of intersection points for real and p-adic surfaces involved contains very few points.

For details see the new chapter Motives and Infinite Primes of "Physics as a Generalized Number Theory" or the article with same title.

MOND and TGD

Sean Carroll writes about breakdown of classical gravity in Cosmic variance. Recall that the galactic dark matter problem arose with the observation that the velocity spectrum of distance star is constant rather than behaving as 1/r as Newton's law assuming that most mass is in the galactic center predicts.

The MOND theory and its variants predict that there is a critical acceleration below which Newtonian gravity fails. This would mean that Newtonian gravitation is modified at large distances. String models and also TGD predict just the opposite since in this regime General Relativity should be a good approximation.

1. The 1/r² force would transform to 1/r force at some critical acceleration of about a=10^-10 m/s²: this is a fraction of 10^-11 about the gravitational acceleration at the Earth's surface.

2. What Sean Carroll wrote about was the empirical study giving support for this kind of transition in the dynamics of stars at large distances and therefore breakdown of Newtonian gravity in MOND like theories.

In TGD framework critical acceleration is predicted but the recent experiment does not force to modify Newton's laws. Since Big Science is like market economy in the sense that funding is more important than truth, the attempts to communicate TGD based view about dark matter have turned out to be hopeless. Serious Scientist does not read anything not written on silk paper.

1. One manner to produce this spectrum is to assume density of dark matter such that the mass inside sphere of radius R is proportional to R at last distances. Decay products of and ideal cosmic strings would predict this. The value of the string tension predicted correctly by TGD using the constraint that p-adic mass calculations give electron mass correctly.

2. One could also assume that galaxies are distributed along cosmic string like pearls in necklace. The mass of the cosmic string would predict correct value for the velocity of distant stars. In the ideal case there would be no dark matter outside these cosmic strings.
   1. The difference with respect to the first mechanism is that this case gravitational acceleration would vanish along the direction of string and motion would be free motion. The prediction is that this kind of motions take place along observed linear structures formed by galaxies and also along larger structures.

   2. An attractive assumption is that dark matter corresponds to phases with large value of Planck constant is concentrated on magnetic flux tubes. Holography would suggest that the density of the magnetic energy is just the density of the matter condensed at wormhole throats associated with the topologically condensed cosmic string.
   3. Cosmic evolution modifies the ideal cosmic strings and their Minkowski space projection gets gradually thicker and thicker and their energy density - magnetic energy - characterized by string tension could be affected

TGD option differs from MOND in some respects and it is possible to test empirically which option is nearer to the truth.

1. The transition at same critical acceleration is predicted universally by this option for all systems-now stars- with given mass scale if they are distributed along cosmic strings like like pearls in necklace. The gravitational acceleration due the necklace simply wins the gravitational acceleration due to the pearl. Fractality encourages to think like this.

2. The critical acceleration predicted by TGDr depends on the mass scale as a ∝ GT²/M, where M is the mass of the object- now star. Since the recent study considers only stars with solar mass it does not allow to choose between MOND and TGD and Newton can continue to rest in peace in TGD Universe. Only a study using stars with different masses would allow to compare the predictions of MOND and TGD and kill either option or both. Second test distinguishing between MOND and TGD is the prediction of large scale free motions by TGD option.

TGD option explains also other strange findings of cosmology.

1. The basic prediction is the large scale motions of dark matter along cosmic strings. The characteristic length and time scale of dynamics is scaled up by the scaling factor of hbar. This could explain the observed large scale motion of galaxy clusters -dark flow- assigned with dark matter in conflict with the expectations of standard cosmology.

2. Cosmic strings could also relate to the strange relativistic jet like structures meaning correlations between very distant objects. Universe would be a spaghetti of cosmic strings around which matter is concentrated.

3. The TGD based model for the final state of star actually predicts the presence of string like object defining preferred rotation axis. The beams of light emerging from supernovae would be preferentially directed along this lines- actually magnetic flux tubes. Same would apply to the gamma ray bursts from quasars, which would not be distributed evenly in all directions but would be like laser beams along cosmic strings.

For more about TGD based vision about cosmology and astrophysics see the chapters of the book Physics in Many-sheeted Space-time.

Motives and infinite primes

In algebraic geometry the notion of variety defined by algebraic equation is very general: all number fields are allowed. One of the challenges is to define the counterparts of homology and cohomology groups for them. The notion of cohomology giving rise also to homology if Poincare duality holds true is central. The number of various cohomology theories has inflated and one of the basic challenges to find a sufficiently general approach allowing to interpret various cohomology theories as variations of the same motive as Grothendieck, who is the pioneer of the field responsible for many of the basic notions and visions, expressed it.

Cohomology requires a definition of integral for forms for all number fields. In p-adic context the lack of well-ordering of p-adic numbers implies difficulties both in homology and cohomology since the notion of boundary does not exist in topological sense. The notion of definite integral is problematic for the same reason. This has led to a proposal of reducing integration to Fourier analysis working for symmetric spaces but requiring algebraic extensions of p-adic numbers and an appropriate definition of the p-adic symmetric space. The definition is not unique and the interpretation is in terms of the varying measurement resolution.

The notion of infinite prime has gradually turned out to be more and more important for quantum TGD. Infinite primes, integers, and rationals form a hierarchy completely analogous to a hierarchy of second quantization for a super-symmetric arithmetic quantum field theory. The simplest infinite primes representing elementary particles at given level are in one-one correspondence with many-particle states of the previous level. More complex infinite primes have interpretation in terms of bound states.

1. What makes infinite primes interesting from the point of view of algebraic geometry is that infinite primes, integers and rationals at the n:th level of the hierarchy are in 1-1 correspondence with rational functions of n arguments. One can solve the roots of associated polynomials and perform a root decomposition of infinite primes at various levels of the hierarchy and assign to them Galois groups acting as automorphisms of the field extensions of polynomials defined by the roots coming as restrictions of the basic polynomial to planes x_n=0, x_n=x_n-1=0, etc...

2. These Galois groups are suggested to define non-commutative generalization of homotopy and homology theories and non-linear boundary operation for which a geometric interpretation in terms of the restriction to lower-dimensional plane is proposed. The Galois group G_k would be analogous to the relative homology group relative to the plane x_k-1=0 representing boundary and makes sense for all number fields also geometrically. One can ask whether the invariance of the complex of groups under the permutations of the orders of variables in the reduction process is necessary. Physical interpretation suggests that this is not the case and that all the groups obtained by the permutations are needed for a full description.

3. The algebraic counterpart of boundary map would map the elements of G_k identified as analog of homotopy group to the commutator group [G_k-2,G_k-2] and therefore to the unit element of the abelianized group defining cohomology group. In order to obtains something analogous to the ordinary homology and cohomology groups one must however replaces Galois groups by their group algebras with values in some field or ring. This allows to define the analogs of homotopy and homology groups as their abelianizations. Cohomotopy, and cohomology would emerge as duals of homotopy and homology in the dual of the group algebra.

4. That the algebraic representation of the boundary operation is not expected to be unique turns into blessing when on keeps the TGD as almost topological QFT vision as the guide line. One can include all boundary homomorphisms subject to the condition that the anticommutator δⁱ_kδ^j_k-1+δ^j_kδⁱ_k-1 maps to the group algebra of the commutator group [G_k-2,G_k-2]. By adding dual generators one obtains what looks like a generalization of anticommutative fermionic algebra and what comes in mind is the spectrum of quantum states of a SUSY algebra spanned by bosonic states realized as group algebra elements and fermionic states realized in terms of homotopy and cohomotopy and in abelianized version in terms of homology and cohomology. Galois group action allows to organize quantum states into multiplets of Galois groups acting as symmetry groups of physics. Poincare duality would map fermionic creation operators to annihilation operators and vice versa and the counterpart of pairing of k:th and n-k:th homology groups would be inner product analogous to that given by Grassmann integration.The interpretation in terms of fermions turns however to be wrong and the more appropriate interpretation is in terms of Dolbeault cohomology applying to forms with homomorphic and antiholomorphic indices.

5. The intuitive idea that the Galois group is analogous to 1-D homotopy group which is the only non-commutative homotopy group, the structure of infinite primes analogous to the braids of braids of braids of ... structure, the fact that Galois group is a subgroup of permutation group, and the possibility to lift permutation group to a braid group suggests a representation as flows of 2-D plane with punctures giving a direct connection with topological quantum field theories for braids, knots and links. The natural assumption is that the flows are induced from transformations of the symplectic group acting on δ M²_+/-× CP₂ representing quantum fluctuating degrees of freedom associated with WCW ("world of classical worlds"). Discretization of WCW and cutoff in the number of fermion modes would be due to the finite measurement resolution. The outcome would be rather far reaching: finite measurement resolution would allow to construct WCW spinor fields explicitly using the machinery of number theory and algebraic geometry.

6. A connection with operads is highly suggestive. What is nice from TGD perspective is that the non-commutative generalization homology and homotopy has direct connection to the basic structure of quantum TGD almost topological quantum theory where braids are basic objects and also to hyper-finite factors of type II₁. This notion of Galois group makes sense only for the algebraic varieties for which coefficient field is algebraic extension of some number field. Braid group approach however allows to generalize the approach to completely general polynomials since the braid group make sense also when the ends points for the braid are not algebraic points (roots of the polynomial).

This construction would realize thge number theoretical, algebraic geometrical, and topological content in the construction of quantum states in TGD framework in accordance with TGD as almost TQFT philosophy, TGD as an infinite-D geometry, and TGD as a generalized number theory visions.

This picture leads also to a proposal how p-adic integrals could be defined in TGD framework.

1. The calculation of twistorial amplitudes reduces to multi-dimensional residue calculus. Motivic integration gives excellent hopes for the p-adic existence of this calculus and braid representation would give space-time representation for the residue integrals in terms of the braid points representing poles of the integrand: this would conform with quantum classical correspondence. The power of 2π appearing in multiple residue integral is problematic unless it disappears from scattering amplitudes. Otherwise one must allow an extension of p-adic numbers to a ring containing powers of 2π.

2. Weak form of electric-magnetic duality and the general solution ansatz for preferred extremals reduce the Kähler action defining the Kähler function for WCW to the integral of Chern-Simons 3-form. Hence the reduction to cohomology takes places at space-time level and since p-adic cohomology exists there are excellent hopes about the existence of p-adic variant of Kähler action. The existence of the exponent of Kähler gives additional powerful constraints on the value of the Kähler fuction in the intersection of real and p-adic worlds consisting of algebraic partonic 2-surfaces and allows to guess the general form of the Kähler action in p-adic context.

3. One also should define p-adic integration for vacuum functional at the level of WCW. p-Adic thermodynamics serves as a guideline leading to the condition that in p-adic sector exponent of Kähler action is of form (m/n)^r, where m/n is divisible by a positive power of p-adic prime p. This implies that one has sum over contributions coming as powers of p and the challenge is to calculate the integral for K= constant surfaces using the integration measure defined by an infinite power of Kähler form of WCW reducing the integral to cohomology which should make sense also p-adically. The p-adicization of the WCW integrals has been discussed already earlier using an approach based on harmonic analysis in symmetric spaces and these two approaches should be equivalent. One could also consider a more general quantization of Kähler action as sum K=K₁+K₂ where K₁=rlog(m/n) and K₂=n, with n divisible by p since exp(n) exists in this case and one has exp(K)= (m/n)^r × exp(n). Also transcendental extensions of p-adic numbers involving n+p-2 powers of e^1/n can be considered.

4. If the Galois group algebras indeed define a representation for WCW spinor fields in finite measurement resolution, also WCW integration would reduce to summations over the Galois groups involved so that integrals would be well-defined in all number fields.

p-Adic physics is interpreted as physical correlate for cognition. The so called Stone spaces are in one-one correspondence with Boolean algebras and have typically 2-adic topologies. A generalization to p-adic case with the interpretation of p pinary digits as physically representable Boolean statements of a Boolean algebra with 2ⁿ>p>p^n-1 statements is encouraged by p-adic length scale hypothesis. Stone spaces are synonymous with profinite spaces about which both finite and infinite Galois groups represent basic examples. This provides a strong support for the connection between Boolean cognition and p-adic space-time physics. The Stone space character of Galois groups suggests also a deep connection between number theory and cognition and some arguments providing support for this vision are discussed.

For details see the new chapter Motives and Infinite Primes of "Physics as a Generalized Number Theory" or the article with same title.

PAMELA anomaly suggests a scaled up variant of electro-hadron physics

Resonaances tells that the Fermi collaboration confirms the claim of PAMELA collaboration about anomalous e⁺e^- pairs in cosmic ray radiation. The announcement of Pamela was my second birthday gift at October 30 for two and half years ago. The first gift was CDF anomaly which found a beautiful explanation in terms of tau-pions and the p-adically scaled up variants with color tau- lepton having mass scale by power of two. The tau-pion of mass about 14 GeV decaying in cascade like manner to lower octaves of basic tau-pion explained elegantly the observations reported by CDF. Helsinki University remembered me by giving a third and really lovely gift by banishing me from University. I understand the motivations: I had repeatedly and without careing about warnings of the authorities broken the Basic Principle of Serious Science: You ought to do nothing for the first time.

For some time ago the dilemma posed by the contradictory claims of DAMA and Cogent collaborations on one hand and XENON100 collaboration on one hand finds also nice solution in terms of 14 GeV taupion decaying to charged taupions with mass about 7 GeV. See the previous posting.

The decays of electro-pions to gamma pair can explain the observed anomalous gammas from galactic nucleus with energy very nearly to electron rest mass. Could one understand also the anomalous positrons reported by PAMELA as decay products of lepto-pion like states, say tau-pions? Intriguingly, the first figures of the article by Alessandro Strumia discussing the constraints on the possible explanations of the PAMELA anomaly show that the anomalous positron excess starts around 10 GeV, possible it starts already at 7 GeV. It is not possible to say anything certain below 10 GeV since the measurements are affected by the solar actvity below 10 GeV. What is however clear is that the excess cannot be explained by taupion decays with 14 GeV mass since the excess would be localized around energy of about 7 GeV. Higher mass is required.

The article by Alessandro Strumia summarizes various theoretical constraints on the new particle explaining positron and electron excesses. The conclusions are following.

1. DM should result in a decay of quite a narrow particle with a mass very near to 2M, which is nearly at rest. What narrow means quantitatively is not clear to me.
2. DM should carry a charge mediating long range interaction with the mediating boson which is must lighter than the particle itself: photon is the obvious candidate. Electromagnetically charged dark matter is however in conflict with the standard prejudices about dark matter and actually in dramatic conflict with its basic property of being invisible. Hierarchy of Planck constants is the only solution to the paradox of charged invisible dark matter.
3. DM must prefer the decays to leptons since otherwise there would be also antiproton and proton excess which has not been observed.
4. The mass of DM should be above 100 GeV.

These conditions encourage the idenfication of DM as a decay product of leptopion like state but with mass considerably higher than the 14 GeV mass. Tau-pions could of course be present but would not contribute to the anomaly at energies not too much above 7 GeV. Tau-pions would also give muon pair anomaly. Heavier leptopion like states are required and electropion would be the most natural candidate.

1. If a scaled up variant of ordinary hadron physics characterized by M₈₉ is there as the recent bumps having interpretation as mesons of this physics suggest, there is no deep reason preventing the presence of also the scale variant of leptohadron physics in this scale. Even more, one can argue that colored leptons must appear as both dark and ordinary variants. Dark variants with non-standard value of Planck constant can have masses of ordinary leptons plus possibly their octaves as in the case of tau at least. The decay widths of intermediate gauge bosons require ordinary colored leptons to have mass higher than 45 GeV.

2. The mass of scaled up electropion would be obtained by scaling the mass of the dark electropion which for M₈₉ electro-pion physics is in a good approximation 2m_e=1 MeV by a factor 2^(127-89)/2= 2¹⁹. This gives electropion mass equal to 500 GeV. Ordinary colored electron would therefore have mass of 250 GeV consistent with the lower bound. The conclusion would be rather ironic: we would have seen dark colored electron (in TGD sense) already at seventies and covered it carefelly under the rug and would be seeing now the ordinary colored electron and stubbornly trying to identify it as DM without caring about the fact that if dark matter is invisible in the standard sense it cannot be electromagnetically charged! Nature seems to love vulgar humour and feel no mercy towards pompous theoreticians enjoying monthly salary;-).

3. By stretching one's imagination one might play with the thought that superpartners of colored leptons with mass scale of order 100 GeV could form pion like states. The superpartners decay to partner and neutrino since R-parity is not exact invariance in TGD and all depends on how fast this process occurs.

4. Skeptic could wonder why the counterparts for colored excitations of quarks are not there and induce the increase of proton and antiproton fluxes.

To summarize, entire Zoo of not only new particles but even of new physics could be waiting for us at LHC energies if we live in TGD Universe!

Another approach to primordial cell

In the previous posting I told about the highly interesting work of the group of Martin Hanczyc in attempts to build protocell. Also the group led by Jack. W. Szostak, who was the 2009 Nobel Prize winner in physiology or medicine - has carried out beautiful experiments in which they are able to create a candidate for protocell satisfying many of the basic requirements.

One such condition is the ability of protocell to transfer various nutrient molecules through the protocell membrane. In modern cell pumps and channels consisting of proteins are believed to serve that purpose (for a different view see the remark below). Genetically coded proteins were however absent during the primordial era. Therefore the membrane is constructed of branching lipids believed to exists during prebiotic era allowing sugars which are basic building bricks of DNA to permeate to the protocell. Given the DNA template , the basic building bricks of DNA molecule assemble to a copy of DNA in this protocell.

What is still lacking is the generation of the template strand of DNA itself and also the replication of protocell. If dark DNA in the form of dark nucleon strings is really there, the template could result as the assembly of the basic bricks of DNA around it and above a proposal for the analog of this kind of process is suggested. The replication of the dark genes would have been also present from the beginning and would have preceded the replication of genes and protocell. Biological evolution could be seen as a migration from dark space-time sheets to ordinary ones and somewhat analogous to the migration of life from sea to land.

Remark: There are puzzling experimental findings about quantal currents through cell membrane even in absence of metabolic sources. In many-sheeted space-time one could interpret these currents as various kinds of Josephson currents running between cell interior and exterior along current carrying space-time shees. Pumps and channels would be more like a diagnostic tool allowing cell to measure the concentrations of various important biomolecules and ions.

At first sight the approaches of Szostak and Martin Hanczyc look very different. These approaches have however a lot of common at deeper level if one accepts TGD based view as DNA-cell membrane system or its more primitive version as a topological quantum computer like system relying on the braiding of magnetic flux tubes connecting the counterpart of DNA nucleotides to the lipids of protocell membrane and on the prebiotic realization of genetic code at the level of dark nuclear physics.

One could also argue that the protocell of Hanczyk represents oil based life as opposed to life as we know it. In TGD framework this is a mis-interpretation. The protocells of Hanczyk live in an aqueous environment. Nitrobenzene oil is an aromatic compound as also sugars and contains nitrogen taking in the proposed scenario same role as phosphorus in ordinary life. Oleic anhydride is lipid and- would provide basic building brick for a particular variant of DNA like structure half-way between dark and completely chemical realization. Oleic anhydride would provide also the building bricks of protocell membrane and serve as a nutrient just like fat molecules- also lipids- serve in "real life".

For background see the chapter Evolution in Many-Sheeted Space-time of "Genes and Memes".

Oil droplets as a primitive life form?

The origin of life is one the most fascinating problems of biology. The classic Miller-Urey experiment was carried out almost 60 years ago. In the experiment sparks were shooted through primordial atmosphere consisisting of methane, ammonia, hydrogen and water and the outcome was many of the aminoacids essential for life. The findings raised the optimism that the key to the understanding of the origins of life. After Miller's death 2007 scientists re-examined sealed test tubes from the experiment using modern methods found that well over 20 aminoacids-more than the 20 occurring in life- were produced in the experiments.

The Urey-Miller experiments have yielded also another surprise: the black tar consisting mostly of hydrogen cyanide polymer produced in the experiments has turned out to be much more interesting than originally thought and suggests a direction where the candidates for precursors of living cells might be found. In earlier experiments nitrobenzene droplets doped with oleic anhydride exhibited some signatures of life. The droplets were capable to metabolism using oleic anhydride as "fuel" making for the droplet to move. Droplets can move along chemical gradients, sense each other's presence and react to it and have also demonstrated rudimentary memory. Droplets can even "solve" a maze having "food" at its other end.

The basic objection against identification as primitive life form is that droplets have no genetic code and do not replicate. The model for dark nucleons however predicts that the states of nucleon are in one-one correspondence with DNA, RNA, tRNA, and aminoacid molecule and that vertebrate genetic code is naturally realized. The question is whether the realization of the genetic code in terms of dark nuclear strings might provide the system with genetic code and whether the replication could occur at the level of dark nucleon strings. TGD inspired quantum model of biology leads to a model for oil droplets as a primitive life form. In particular, a proposal for how dark genes could couple to chemistry of oil droplets is developed.

Intelligent oil droplets

New Scientist tells about a new twist related to the Urey-Miller experiment. Martin Hanczyc and his colleagues of University of Southern Denmark in Odense are doing research with a rather ambitious goal: the discovery of the recipe of life. The highly demanding challenge is to find candidates for the protocell that preceded the recent cell. What makes the task so difficult that it is not even clear what one should be searching for. For instance, what basic characteristics distinguishing living matter from inanimate systems protocell is expected to have before one can speak about primitive life form? And if one accepts the dogmas of standard biology, one encounters also the nasty hen-egg question which came first: metabolism or the genetic machinery.

Hanczyc and his colleagues have been experimenting with simple candidates for primitive life forms: oily nitrobenzene droplets doped with oleic anhydride immersed in alkaline aqueous solution (alkalinity is by definition an ability to reduce acidicity). They have found that these systems have some attributes generally associated with life. The recent experiments replaced oleic anhydrite with the black tar consisting of complex branched and fractal looking hydrogen cyanide (HCN) polymer produced by Urey-Miller experiments and found that also now the droplets exhibit lifelike behavior: they sense and respond their neighbors and move towards "food" sources.

The earlier experiments using nitrobenzene droplets doped with oleic anhydridge immersed in alkaline solution began immediately to move along straight lines. What happened that the oleic anhydrite at the surface of the droplet reacted with the water spilitting to two oleic acid molecules by hydration. This dropped the surface tension of the droplet and by a kind of spontaneous symmetry breaking the reaction rate had maximum at some point of the droplet and a "hot spot" was generated drawing oleic anhydride from the interior of the dropled and generating a convective flow. A pH gradient develops along the surface. The oleic acid in turn moved along the droplet surface from the hot spot to the diametrically opposite side of the droplet (see this). The net effect was a linear motion. pH gradient is claimed to be essential for the generation of motion but I must admit that I do not quite understand this point. A primitive metabolism liberating energy is obviously in question. By momentum conservation the total momentum for the convective flow and flow of oleic acid was compensated by a center of mass motion of the droplet.

One could claim that this process belongs to the same class of self-organization processes as the generation of convection patterns as one heats liquid from below. Other researchers have however discovered that the oil droplets can also travel along chemical gradients, something known as chemotaxis used by many bacteria to find food and void threats. One oil droplet managed even to "solve" a complex maze containing "food" at its other end. Whether this kind of behavior can be regarded as a mere chemistry is far from obvious to me. To me this a achievement look like a genuinely goal directed intentional behavior.

Hanczyc has also found that when the oil droplets approach each other they change course to avoid collision, or can circle each other-like partners in Viennese waltz! Oil droplets seem to have even memory. By videoing the paths of oil droplets Hanczyc found that the decision to stop or continue was not random but the behavior at any point of orbits was affected by the earlier behavior. This is by the way an elegant experimental manner to show that non-deterministic behavior is not just randomness. The experiments have been also carried using instead of oleic anhydrige mineral oil consisting of a mixture of alkanes having as building block polymeres from from CH₄ by dropping two hydrogen from each C as also lipids have (methane CH₄ is the simplest alkane). What distinguishes mineral oil molecules from the oleic anhydride molecules are the oxygen atoms in the middle of the reflection symmetric linear molecule. Also now the droplets move although the process takes place with a slower rate.

The basic objections against the identification of the oil droplets as a life form is that they do not replicate and there is no genetic code. One must be however very cautious with this kind of statetments. Maybe the primary life forms are not the droplets and the behavior of droplets reflects the control actions of these life forms on droplets. Perhaps also genetic code could be realized at at totally different level. The recent findings of the group of HIV Nobelist Montagnier indeed suggest a new realization of genetic code in water closely related to to water memory and TGD suggests a concrete realization of this code.

Some key ideas of TGD inspired quantum biology

Before proposing a model for intelligent oil droplets as a primitive life form its good to list some of the basic ideas of TGD inspired quantum biology.,

1. The basic hypothesis is that the dark matter at the magnetic flux tubes of the magnetic body assignable to any physical system serves as an intentional agent controlling the behavior of the ordinary matter (see this). Dark matter can correspond to just the ordinary particles- at least electrons and protons- in a phase with non-standard large value of Planck constant forming macroscopic quantum phases. Also biologically important ions could form this kind of phases.

   TGD inspired nuclear physics (see this) allows also the bosonic counterparts of fermionic with same nuclear charge so that every fermionic ion could be accompanied by exotic bosonic ion so that Bose-Einstein condensates could become possible.

2. The model for dark nucleons as entangled triplets of three quarks (see this and this) leads to the identification of the counterparts DNA, RNA, tRNA, and aminoacids as three-quark states and one can identify also vertebrate genetic code. DNA sequences correspond to dark nucleon sequences - dark nuclei - in this correspondence. The proposal is that dark proton sequences in water form dark nucleons with so large a Planck constant that nucleon size corresponds to size of singe DNA codon. There is indeed evidence that in attosecond time scale (time scale for corresponding causal diamonds) water obeys effective chemical formula H_1.5O as far as scattering of electrons and neutrons is considered (see R. A. Cowley, Physics 350, 243-245, 2004 and R. Moreh et al, Phys Rev. 94, 2005)).

   This would suggest that 1/4 of protons are in dark large Planck constant phase in the experiments. This proportion is expected to depend on temperature and pressure and should explain the rich spectrum of anomalies of water by regarding it as a two phase system (see this). Perhaps these protons could form dark nucleon sequences realizing genetic code. These sequences could replicate and evolve and could define at least the analog of DNA or RNA. Maybe even DNA-mRNa-aminoacids translation processing could take place. If a translation machinery transforming exotic DNA to ordinary has developed during evolution, this fundamental realization of genetic machinery might make possible kind of Research&Development making possible to experiment with different genomes. Evolution would not be a random process anymore (see this).

3. The proposal is that the ordered water layers associated with polar molecules dissolved in water are attached to the magnetic body of the molecule induced in water environment and that this magnetic body mimicking the original molecule is an essential element of this primitive life (see this). The self-organization processes of these layers induced by external perturbations could be the predecessor of processes like protein folding and de-folding. The mechanism of water memory could be based on dropping of the magnetic bodies of molecules as a result of repeated shaking involved with homepathic procedure inducing a sequence of catastrophes driving the evolution of these primitive life forms. One can also ask whethert these magnetic bodies could define the analog of proteins providing one realization of dark matter genetic code.

4. If dark nucleons have been the predecessors of chemical life forms, one can circumvent the hen-egg question about whether the genetic code or metabolism came first. In zero energy ontology negative energy signals propagating in the direction of geometric past would in turn provide fundamental mechanism of intentional action, metabolism, and memory. If this is the case, evolution would have only led to a refinement of the fundamental mechanisms of life already existing: there would be no need to pull anything out of hat. The mechanisms for chemical storage and utilization of energy are needed and moving oil droplets would provide a primitive realization of these mechanisms.

5. The notion of negentropic entanglement makes sense if one accepts the role of p-adic number fields and the vision about life as something residing in the intersection of real and p-adic worlds (see this). Entanglement probabilities for negentropic entanglement must be rational or algebraic numbers in the algebraic extension of p-adic numbers involved and there is unique prime for which this entanglement entropy is maximally negative. Negentropic entanglement makes possible new kind of many particle states which is not based on binding energy but the fact that negentropic entanglement is stable against state function reduction if Negentropy Maximization Principle determines its dynamics also in the case of negentropic entanglement. This makes it possible to have bound state like many particle states in which composite particles are in well-defined sense free and binding energy is formally negative. The proposal is that the mysterious high energy phosphate bond corresponds to negentropic entanglement and carries both metabolic energy and information (see this). In this framework ATP-ADP cycle has also information theoretic interpretation as a transfer of conscious information.

The model for DNA as topological quantum computer (see this and this) led among other things to an identification of magnetic flux tubes connecting bio-molecules as a basic building bricks of living matter.

1. Flux tubes are assumed to connect DNA nucleotides to lipids of the nuclear and cell membranes. Flux tubes could begin from =O in the double bonds R=O or from negatively charged oxygens. In the case of DNA R would correspond to the basic unit in phosphate deoxiribose backbone consisting of aromatic 5-cycle and PO₄ containing one =O and one O^-. The lipid end would would contain =O and -OH and the flux tube could end to either of these or possibly -OH ionized to -O^- by a transformation of proton to dark proton.

2. The braiding of flux tubes makes topological quantum computation like processes possible (see this). The contractions and expansions of flux tubes induced by phase transitions changing the value of Planck constant would be a basic control mechanis allowing to understand how two biomolecules (say DNA and its conjugate) can find each other in the thick soup of organic molecules. The reconnections of the magnetic flux tubes would be second basic control mechanism and ATP→ADP process and its reverse would represent standardized reconnection.

3. The flux tube ends would contain quark and antiquark (u,d and their antiquarks are involved) coding for the four DNA letters A,T,C,G so that also dark quarks and their antiquarks would provide an elementary particle level realization for the codons. Note that topological quantum computation does not necessitate genetic code and therefore also the repeating DNA sequences regarded as junk could be used for topological quantum computations.

General ideas about oil droplets as a primitive life form

It is interesting to see what one obtains if one takes the dark nucleon realization of genetic code, the mechanism of water memory realized as magnetic bodies attached to the ordered water layers associated with polar molecules, the model for DNA as topological quantum computer, and the ideas about magnetic body with dark matter as fundamental bio-control as basic ingredients of the model of intelligent oil droplets.

1. A process resembling spontaneous symmetry breaking occurs for the droplet molecules as the hot spot is formed. The interpretation as a generation of magnetic body of approximately dipolar magnetic field is attractive. The magnetic body would control the droplet. The change of the direction of the motion of the oil droplet would correspond to the change of the orientation of the magnetic body and would thus reduce to a motor action of the magnetic body.

2. The flux tubes of the magnetic body would be most naturally parallel to the direction of the nitrobenzene polymer strands. Oleic anhydride molecules and the hydrogen cyanid polymers would be transferred along the magnetic flux tubes of an approximately dipolar magnetic field entering to the hot spot from interior and the oleic acid molecules could move along the flux tubes continuing along the surface of the droplet to the diametrically opposite point. The migration of birds along magnetic field lines is a fractal analog for this.

3. The dark matter at the magnetic body would give the oil drop its "intelligence". The dark nuclear genome could be realized at the magnetic body and the magnetic bodies might define the replicating life form as in the TGD based model of water memory for which the magnetic bodies represent molecules as far as low frequency electromagnetic fields characterized by cyclotron frequencies are considered. One could see intelligent oil droplets as a manifestation of control actions of a life form defined by dark matter at magnetic flux tubes and the first step in the process eventually leading to a complex control and coordination of the behavior of ordinary matter.

4. The ability of droplets to react to the presence of other droplets would be due to the communications between magnetic bodies based on low frequency photons at cyclotron frequencies but having energy above thermal energy if the value of Planck constant is large enough.

At least oleic anhydrite, hydrogen cyanide, and mineral oil can serve as a fuel of oil droplets and this raises the question what might be the common property shared by them. Certainly this property must relate to metabolism and the model for ordinary metabolism suggests that this property is shared also by the high energy phosphate bond.

1. Oleic anhydrite is a lipid formed by as a fusion of two oleic acids consisting of a sequence of CH₂ units and the characteristic (C=O)-(O-H) group at its end. The burning of the molecule splits it to two oleic acids by hydration meaning utilizing one water molecule. The formation of oleic acid in turn involves dehydration so that the burning process is analogous to depolymerization of DNA or aminoacid sequence by hydration.

2. Mineral oil is also a lipid and looks like oleic anhydride locally. In the ideal case however the crucial ..(C=O)-O-(C=O)-.. portions are lacking. Oxygenation could however produce this kind of defects to the mineral oil molecules so that the mechanism of burning would remain the same.

3. Hydrogen cyanide HCN involves valence bond of valence 3 between C and N. The polymers are constructed from H-C-N sequences with single valence bond between both C:s and N:s of two subsequent horizontal H-C-N units, which one can think of as being obtained from (H-C)-(H-C)... sequence and ..N-N-N... sequences with N and C connected by horizontal bonds. This polymer replaces oleic acid as a "fuel" reacting with water and liberating metabolic energy. These polymers -which would serve as primitive analogs of proteins- would be transferred along the magnetic flux tubes and burned at the hot spot by hydration. HCN has been proposed to have been a primitive precursor of both amino acids and nuclei acids. With motivations coming from the general vision about quantum biology, tt will beproposed that also hydrogen cyanide polymers contain in their C-backbone ..(C=O)-O-(C=O)-.. portions as local defects due to oxygenation so that the burning would occur via hydration in all three cases.

What are the prerequisites for metabolism and topological quantum computation like processes?

The basic question is whether metabolism interpreted in TGD framework as negentropy transfer and thus requiring the analogs of high energy phosphate bond and ATP-ADP cycle is possible. The high energy phosphate bonds make also possible flux tube structures serving as a prerequisite for topological quantum computation like process. Both oleic anhydride, hydrogen cyanide and mineral oil can serve as a metabolic source and one should identify the common property of them making. This property should be the analog of high energy phosphate bond.

1. High energy phosphate bond carries metabolic energy. This bond is poorly understood and I have proposed that high energy phosphate bond carries negentropic entanglement identified as the basic characteristic of life (see this. In the middle of oleic anhydride there =O-O-=O structure and its splitting in hydration liberates energy. This suggests that this structure also now carries the negentropic entanglement and the metabolic energy. The splitting process of oleic anhydrite occurring at the hotspot would be analogous to ATP→ ADP process involving splitting of PO₄ molecule from ATP.

2. Oleic acid is a lipid containing at its second end the characteristic (C=O)-OH group assumed to serve as a terminal for the magnetic flux tubes in the model of DNA-cell membrane system as quantum computer. In the presence energy feed one could imagine that the inverse process transforming oleic acid to oleic anhydride takes place and a primitive version of the metabolic cycle involving photosynthesis and cellular breathing can be imagined. Metabolic and quantum information processing would be very intimately related. By DNA as topological quantum computer analogy the magnetic flux tubes connecting oleic anhydride molecules would make be responsible for primitive topological quantum computation if present in the system.

3. Also when the tar from Urey-Miller experiment replaces oleic anhydrite small amount of oleic anhydride was used to build a film around oil droplet to lower surface tension. This suggests that the oleic anhydride has a deeper purpose and defines the analog of cell membrane and make possible for the magnetic flux tubes from the interior of the droplet to attach to the lipids? This could occur at least in the hot spot and at point opposite to it so that magnetic flux tubes would connect the diametrically opposite points of the droplet. Oleic anhydride would therefore serve a dual purpose serving both asa metabolic resource and a building brick of the protocell membrane: metabolic energy would be accompanied by information. Also in real life lipids -about which fats are a special case- have this double role.

4. The process occurs for both for hydrogen cyanide and mineral oil and and this raises obvious objections against the model since the energy and information carrying =O-C-O-C=O structures making also possible the flux tube connects are not present in the ideal situation. One must however remember that the situation in real life is far from ideal and the most obvious idea is that the polymers as such are not enough: oxygen is the basic metabolic resource and oxygenation serving as the loading of metabolic batteries might be the crucial element.
   1. The backbone of both lipids and of mineral oil polymers is CH₂ sequence. If some fraction of mineral oil polymers contain (C=O)-O -(C=O):s serving as carriers of metabolic energy and information the situation reduces to that for oleic anhydride apart from effects caused by the fact that the density of metabolic energy per volume is expected to be lower, which would explain why the motion is slower.
   2. Also in the case of hydrogen cyanide polymers one can imagine the presence of similar defect structures due to oxygenation. A portion of ...(H-C)-(H-C)-(H-C).... sequence would be replaced with ....(H-C)-(C=O)-O-(C=O)-(H-C)... with three carbons lacking. The nitrogen sequence ...N-N-N-N-N.. would split to ...N-OH and OH-N... so that three nitrogens would be lacking.

Under these assumptions the model explains all three cases using hydration as the basic mechanism of metabolism as well as the conditions required by DNA as topological quantum computer model. Note that the process consumes oxygen just as the ordinary breathing.

What about genetic code and counterpart of DNA?

Consider next the possible realization of the genetic code. The first thing to notice is that even in the case that genetic code is not realized the braiding would make possible topological quantum computation like processes and a realization of memory in terms of braiding patterns. Furthermore, chemical realization of the genetric code is not possible so that dark nucleons remain the only possibility in TGD framework. The challenge is to try imagine whether DNA like structures having flux tube connections with the counterparts of lipids in the cell membrane could exist. The following suggestion is a product of free imagination based on analogies and reflects my amateurish skills in biochemistry.

1. Aromatic rings are an essential element of both phosphate deoxiribose backbone of DNA and of DNA letters itself. Nitrobenzene molecule obeys chemical formula (C₆H-5)-NO₂ and contains benzene ring to which NO₂ nitro group is attached. The oily character is due to the benzene ring. Benzene rings could serve as a counterpart for the hydrocarbon 5-cycles appearing in phosphate deoxiribose backbone. Note however that in deoxiribose ring one carbon is replaced with O and two hydrogens with OH. Moreover, single benzene molecule would correspond to the counterpart of DNA triplet rather than single nucleoside. One could however argue that only a backbone is in question so that the differences might not matter.

2. One would naively expect that both nitrogen and phosphorus have same valence equal to three. In PO₄ phosporus has 5 valence bonds as a rule and the interpretation is that phosphorus tends to donate its valence electrons to get empty shell. This kind of states are known as oxidation states and are possible also for nitrogen: hydroxylamine NO₂H is one exmple of this kind of state. In fact, from the from structural formula of nitrobenzene one finds that nitrogen gives one electron to second oxygen so that also this state can be regarded as an oxidation state. This inspires the idea that nitrogen takes the role of phosphorus at least partially.

3. If one does not allow oxidation states, the simplest manner to construct the analog of phosphate deoxiribose backbone is as structure ...X-X-X..., with X= R-O- (R₁-N)-O, where R denotes oleic anhydride and R₁ is for benzene residue. The bridges connecting benzene rings would be reflection symmetric. The breaking of reflection symmetry is however essential since it determines the reading direction of DNA.

4. If one accepts oxidation states, the simplest option is that in benzene-NO₂ complex NO₂ is replaced with (N=0)-O and the counterpart of phosphate deoxiribose backbone would have the structure ...X-X-X-..., X=R- (R₁-N=0)-O with R denoting oleic anhydride and R₁ benzene. Oleic anhydride has valence bond to N so that N has 5 valence bonds as phosphorus in phosphate. Also the crucial =O is present. The units connecting subsequent benzene rings are not reflection symmetric anymore as indeed required. There is however no charged oxygen as in the case of ordinary DNA. Note that the analogs for AMP, ADP, ATP make sense since one can single replace P by N phosphate PO₄.

5. An interesting question is whether the nitrogen based metabolism could be realized as a primordial metabolism. Nitroglycerin is analogous to tri-phosphate although the nitrates are not arrranged linearly as in ATP and is used as both heart medicine and as an active incredient of explosives. The latter use conforms with the idea about the presence of high energy nitrate bond in NO⁴.
6. The two mirror image branches of oleic anhydride molecule consist of 15 carbon atoms and the structure is rather long as compared to the basic unit of phosphat edeoxiribose backbone so that the distance between subsequent benzene units would be rather long- of order 10 Angstroms. On the other hand, 10 DNA codons correspond to 10 nm length in a good accuracy so that one codon would take 1 nm length also in this case. If double strand is formed, twisting is possible so that the scales could be the same. The size scale of the dark nucleon representing single DNA codon should correspond to the size scale of single oleic anhydride molecule and the required value of Planck constant would be of order 10⁶ as the ratio of this scale and nucleon size of order 10^-15 meters.

7. The counterparts of DNA nucleotides forming a linear structure should join to the benzene rings. Dark nucleon sequences remain the only possibility if one wants a realization of genetic code. Each dark codon represented by dark nucleon would be connected by three flux tubes with quark and antiquark at their ends to single unit of the proposed structure. There would be three =O:s per single benzene ring. Since single benzene ring corresponds to single DNA codon three =O:s are indeed expected. Therefore =O:s could indeed correspond to terminals for flux tubes coming from single dark nucleon representing single DNA codon.

8. The division of oil droplet would be the analog of cell replication and would involve at the deeper level the replication of dark nucleon sequences. This requires the analog of DNA double strand and the analogs of DNA codons would be dark nucleons. Genetic codons could be realized in terms of flux tubes connecting dark nucleon sequences to the oleic acids or oleic anhydrides at the surface of the droplet. It remains to be seen whether the division can be achieve in real world.

To sum up, this model is rather direct application of TGD based vision about life and the killer test is whether the mineral oil oil molecules and hydrogen cyanide molecules are not ideal but actually contain the (C=O)-O-(C= O) pieces carrying energy and information and serve as terminals for the magnetic flux tubes.

For background see the chapter Evolution in Many-Sheeted Space-time of "Genes and Memes". See also the article Oil droplets as a primitive life form?

ATLAS detects nothing in 110-150 GeV energy range

The rumor about 115 GeV bump found by ATLAS and interpreted as photo-philic Higgs caused much fuss in physics blogs. Now ATLAS has published a note in which the situation is finally settled: there is absolutely nothing more than the standrard model background in the energy regions in the energy range 100-150 GeV.

Lubos gives an official version of this previous report about the invalidity of 115 GeV Higgs but forgets to give link to his first posting in which he reveals that he has all the time predicted the Higgs mass to be 115 GeV and this is the most accurate and robust prediction of supersymmetry! Lubos also told in my blog that superstringers have no problem in increasing by a factor 30 the predicted decay width of Higgs to photon-pair: with this I could not but agree since in an emergency situation a good theoretician is always able to generate few orders of magnitude from his back pocket. I have regarded Lubos as a rather hard wired theorist but this sudden change of deepest convictions suggests just the opposite!

I think that many of his readers have had the suspision that maybe Lubos is after all right about the non-existence of man-made climate change, about the intellectual inferiority of women, about criminal character of all leftists and environmental activists, and so on. Perhaps this episode gives an opportunity to re-estimate the intellectual honesty of Lubos about which he makes so much fuss.

For me ATLAS bump was not so well-come event for me and as a proponent of a new hadron physics I would have been much happier just with following bumps (see the previous posting).

1. The 145 GeV bump having interpretation as charged pion of M₈₉(=2⁸⁹-1) physics. Note that the neutral pion of this physics is just at the upper end of the region scanned by ATLAS and found to be empty of di-photons.
2. The 325 GeV bump reported by D0 suggesting interpretation in terms of charged kaon of this physics.
3. The 324.8 GeV and 325 GeV CDF bumps having possibly interpretation in terms of decays of short and long lived neutral kaons of new hadron physics.

The problem is that the mass scale of CP and maybe also CPT breaking would be enormous as compared to that in ordinary kaon-antikaon system system which is is of order 10^-6 eV and in zero energy ontology could have an interpretation in terms of secondary p-adic mass scale assignable to the space-timeh sheets of ordinary hadrons characterized by M₁₀₇. On the other hand, it is easier to imagine such a gigantic breaking if the 4 GeV top-antitop mass splitting reported by D0 is real since it means enormous CPT breaking with size scale of electromagnetic corrections.

Perhaps it is not an accident that the mass splitting of .2 GeV for M₈₉ neutral kaon would rather accurately correspond to the p-adic mass scale assignable to the space-time sheet of hadrons characterized by M₁₀₇. In TGD space-time hadrons contain hadrons inside them and quarks contain quarks inside them. Could the topological condensation of M₈₉ hadronic space-time sheets at M₁₀₇ hadronic space-time sheets be responsible for the mass splitting as splittings caused by interactions with environment rather than as radiative corrections as in the case of kaon and B meson? If so, the large CP breaking could be long length scale phenomenon rather than short distance phenomenon although the scale of breaking would suggest just the opposite.

A hint about the underlying short and long distance mechanisms of CP breaking comes from the following observation.

1. Sea quarks with masses in MeV range and also the valence quarks (u and d) which could also appear inp-adic length scales corresponding to masses of order 100 MeV, have mass smaller than hadron mass and therefore longer Compton length. Thus one encounters a rather strange situation possible only in the quantal world: part can be larger than whole!

   This can be however understood. The space-time sheets of quarks lighter than hadron can be assigned to the color magnetic body of the hadron. This leads to a model for the anomalously large charge radius of proton implied by the measured value of the Lamb shift of muonic atom (see this).

2. Top quark has mass much larger than hadron size and has Compton length smaller than hadron size and thus respects our everyday thinking about the relation between parts and wholes.

This raises questions:

1. Could it be that quarks which size smaller than hadron size suffering topological condensation on hadrons experience large CP and CPT breaking with the scale of mass splittings characterized by the p-adic mass scale of the hadron?
2. If the quark's Compton size is larger than that of hadron quark suffers topological condensation on the field body of hadron: in the case of kaon this would predict correct order of magnitude for the mass splitting which is near the lower bound. The standard description in terms of short distance radiative corrections coming from quark loops with large quark masses should be consistent with this description.
3. Neutral B-meson finds itself in a schizophrenic situation: b quark is smaller that and s quark larger than hadron! Hence b quark should condense at the hadronic space-time sheet and d quark at the field body of hadron. B meson has its feet at different space-times! Note however that the valence quarks are connected by color flux tube so that poor B does not split to two pieces. Could this allow also to understand why the CP breaking in B-Bbar system is 50 times larger than predicted by the standard model but not so gigantic that the mass splitting for top quark?

Zero energy ontology leads to a TGD based modification of entropic gravity suggesting also a more concrete view abot the breaking of discrete symmetries.

1. Gravitons are still there but in thermal equilibrium at flux tubes along which their travel and also photons are in similar thermal equilibrium so all interactions are entropic in TGD sense as the vision about quantum theory as a square root of thermodynamics suggests.
2. Entropic gravity and electromagnetism would provide a phenomenological view about what happens and would also suggests a general view about how discrete symmetries break down. Charged matter and antimatter could obey different arrow of geometric time by the requirement of thermal stability (temperatures are proportional to the normal component of electric field have opposite sign for charged particle and antiparticle).
3. The arrow of geometric time is a property of zero energy states rather than dynamics and realized as a property of M-matrix for which states are localized with respect to various quantum numbers (in particular particle- and fermion numbers) at the second end of the causal diamond defining the counterpart of initial state).

For details see the article TGD inspired vision about entropic gravitation.

Support for the notion of magnetic flux tube

The notion of magnetic flux tube as space-time sheet is one of the key concepts of TGD and represents a special case of topological field quantization forced by the notion of induced gauge field. This notion is especially relevant for the applications of TGD to quantum biology but is central also for TGD inspired cosmology. Therefore it is encouraging that the empirical support for the notion is accumulating.

The latest news tells about strange cosmic ray hot spots observed in southern sky by Icecube neutrino detector at South Pole. Cosmic muons with median energy of 20 TeV seem to come from certain preferred hotspots, and one can assign to a particular hotspot to the direction of the Vela supernova remnant with a distance of about 1000 light years. The problem is that Vela is so distant that the muons should be deflected in galactic magnetic fields so that all information about the direction should be lost. The hot spot property would require a distance smaller than .03 light years and it is very difficult to imagine anything like this since even the nearest star is at distance of 4 light years.

One of the proposed explanations (by Felix Aharonian) is that the cosmic ray flux indeed arrives along magnetic flux tube channelling the cosmic ray flux. This notion has however now justification in standard physics context. Many-sheeted space-time of TGD is needed.

Second explanation proposed for the muonic hot spots is that there is particle accelerator in the solar scale. Also this explanation has a TGD variant. There is experimental evidence for anomalously high accelerations from lightnings. The energies gained by electrons are above MeV. This is completely out of question in standard physics since the friction of the atmosphere implies that electrons dissipate their energy. Again mainstream manages in an admirable manner to forget facts which could mean revolution in theoretical physics. TGD explanation is in terms of large values of Planck constant reducing friction dramatically. Also now magnetic flux tubes would be the places where dark electrons accelerate in the electric field between the cloud and Earth. If this acceleration mechanism is at work for muons it might explain the hot spots. Energies would be enormous- by a factor of 10⁶ higher than the energies gained by electrons from thunderclouds.

Topological field quantization involves also the notion is topological light ray representing the analog of laser beam at the level of space-time topology, and I have proposed for more than decade ago an explanation of extremely high energy gamma rays arriving from quite too large distances in terms of topological light rays. In this case the scattering from microwave background should have caused the loss of the information about direction and confinement inside topological light ray prevents this.

The difficult political problem is that TGD is officially decided to be a crackpot theory so that no one in his right mind dares to mention the existence of TGD in public space. The consequences of this long term policy are becoming manifest in experimental particle physics with the rate of one hype per week. In the lack of a theory able to really predict something, the experimentalists use their time and resources to either kill the ad hoc models cooked up by phenomenologists or by imagining that they have verified one of the very few almost-predictions that hegemony is able to make. ATLAS rumor was a good example of this. Situation is absurd but nothing can be done since the old men at the top of the power ladder will not give up.

The puzzling situation in dark matter searches

Sean Carroll has explained in Cosmic Variance the latest rather puzzling situation in dark matter searches. Some experiments support the existence of dark matter particles with mass of about 7 GeV, some experiments exclude them. The following arguments show that TGD based explanation allows to understand the discrepancy.

How to detect dark matter and what's the problem?

Consider first the general idea behind the attempts to detect dark matter particles and how one ends up with the puzzling situation.

1. Galactic nucleus serves as a source of dark matter particles and these one should be able to detect. There is an intense cosmic ray flux of ordinary particles from galactic center which must be eliminated so that only dark matter particles interacting very weakly with matter remain in the flux. The elimination is achieved by going sufficiently deep underground so that ordinary cosmic rays are shielded but extremely weakly interacting dark matter particles remain in the flux. After this one can in the ideal situation record only the events in which dark matter particles scatter from nuclei provided one eliminates events such as neutrino scattering.
2. DAMA experiment does not detect dark matter events as such but annual variations in the rate of events which can include besides dark matter events and other kind of events. DAMA finds annual variation interpreted as dark matter signal since other sources of events are not expected to have this kind of variation. Quire recently also CoGENT reported the annual variation with 2.8 sigma confidence level (official report was represented at thursday in STSI Symposium). The mass of the dark matter particle should be around 7 GeV rather than hundreds of GeVs as required by many models. An unidentified noise with annual variation having nothing to do with dark matter could of course be present and this is the weakness of this approach.
3. For a few weeks ago we learned that XENON100 experiment detects no dark matter. Also CDMS results exclude dark matter particles with masses around 7 GeV. According to Sean Carroll, the detection strategy used by XENON100 is different from that of DAMA: individual dark matter scatterings on nuclei are detected. This is a very significant difference which might explain the discrepancy since the theory laden prejudices about what dark matter particle scattering can look like, could eliminate the particles causing the annual variations. For instance, these prejudices are quite different for the habitants of the main stream Universe and TGD Universe.

TGD based explanation of the DAMA events and related anomalies

I have commented earlier the possible interpretation of DAMA events in terms of tau-pions. The spirit is highly speculative.

1. Tau-pions would be identifiable as the particles claimed by Fermi Gamma Ray telescope with mass around 7 GeV and decaying into tau pairs so that one could cope with several independent observations instead of only single one.
2. Recall that the CDF anomaly gave for two and half years ago support for tau-pions whereas earlier anomalies dating back to seventies give support for electro-pions and mu-pions. The existence of these particles is purely TGD based phenomenon and due to the different view about the origin of color quantum numbers. In TGD colored states would be partial waves in CP₂ and spin like quantum numbers in standard theories so that leptons would not have colored excitations.
3. Tau-pions are of course highly unstable and would not come from the galactic center. Instead, they would be created in cosmic ray events at the surface of Earth and if they can penetrate the shielding eliminating ordinary cosmic rays they could produce events responsible for the annual variation caused by that for the cosmic ray flux from galactic center.

Can one regard tau-pion as dark matter in some sense? Or must one do so? The answer is affirmative to both questions on both theoretical and experimental grounds.

1. The existence of colored variants of leptons is excluded in standard physics by intermediate gauge boson decay widths. They could however appear as states with non-standard value of Planck constant and therefore not appearing in same vertices with ordinary gauge bosons so that they would not contribute to the decay widths of weak bosons. In this minimal sense they would be dark and this is what is required in order to understand what we know about dark matter.

   Of course, all particles can in principle appear in states with non-standard value of Planck constant so that tau-pion would be one special instance of dark matter. For instance, in living matter the role of dark variants of electrons and possibly also other stable particles would be decisive. To put it bluntly: in mainstream approach dark matter is identified as some exotic particle with ad hoc properties whereas in TGD framework dark matter is outcome of a generalization of quantum theory itself.

2. DAMA experiment requires that the tau-pions behave like dark matter: otherwise they would never reach the strongly shielded detector. The interaction with nuclei of detector would be preceded by a transformation to a particle-tau-pion or something else- with ordinary value of Planck constant.

TGD based explanation for the dark matter puzzle

The criteria used in experiments to eliminate events which definitely are not dark matter events - according to the prevailing wisdom of course -dictates to high degree what interactions of tau pions with solid matter detector are used as a signature of dark matter event. It could well be that the criteria used in XENON100 do not allow the scatterings of tau-pions with nuclei. This is indeed the case. The clue comes from the comments of Jester in Resonaances. From a comment of Jester, one learns that Cogent - and also DAMA utilizing the same detections strategy - "does not cut on ionization fraction". Therefore, if dark matter mimics electron recoils (as Jester says) or if dark matter produced in the collisions of cosmic rays with the nuclei of the atmosphere decays to charged particles one can understand the discrepancy.

[By the way, also Lubos has commented the puzzling situation.]

The TGD based model for explaining the more than two years old CDF anomaly indeed explains also the discrepnacy between XENON100 and CDMS on one hand and DAMA and CoGENT on the other hand. Recall that the anomaly was put soon under the rug -presumably because it is so badly in conflict with standard model and its extensions- and I was finally expelled from Helsinki University as a consequence of my troublesome blog activities related to the anomaly. The TGD based model for the CDF anomaly can be found here . See also this blog posting and earlier blog postings and also old What's News at my homepage.

1. To explain the observations of CDF one had to assume that tau-pions and therefore also color excited tau-leptons inside them appear as several p-adically scaled up variants so that one would have several octaves of the ground state of tau-pion with masses in good approximation equal to 3.6 GeV (two times the tau-lepton mass), 7.2 GeV, 14.4 GeV. The 14.4 GeV tau-pion was assumed to decay in a cascade like manner via lepto-strong interactions to lighter tau-pions- both charged and neutral- which eventually decayed to ordinary charged leptons and neutrinos.
2. Also other decay modes -say the decay of neutral tau-pions to gamma pair and to a pair of ordinary leptons- are possible but the corresponding rates are much slower than the decay rates for cascade like decay via multi-tau-pion states proceeding via lepto-strong interactions.
3. Just this cascade would take place also now after the collision of the incoming cosmic ray with the nucleus of atmosphere. The mechanism producing the neutral tau-pions -perhaps a coherent state of them- would degenerate in the collision of charged cosmic ray with nucleus generating strong non-orthogonal electric and magnetic fields and the production amplitude would be essentially the Fourier transform of the "instanton density" E⋅B. The decays of 14 GeV neutral tau-pions would produce 7 GeV charged tau-pions, which would scatter from the protons of nuclei and generate the events excluded by XENON100 but not by DAMA and Cogent.
4. In principle the model predicts to a high degree quantitatively the rate of the events. The scattering rates are proportional to an unknown parameter characterizing the transformation probability of tau-pion to a particle with ordinary value of Planck constant and this allows to perform some parameter tuning. This parameter would correspond to a mass insertion in the tau-pion line changing the value of Planck constant and have dimensions of mass squared.

The overall conclusion is that the discrepancy between DAMA and XENON100 might be interpreted as favoring TGD view about dark matter and it is fascinating to see how the situation develops. This confusion is not the only confusion in recent day particle physics. All believed-to-be almost-certainties are challenged. To be honest (I am unable to be anything else): I have the feeling that TGD vision is what survives after we wait for a decade or two;-).

For TGD based model for CDF anomaly in terms of colored excitations of tau lepton and the earlier anomalies in terms of colored electrons and muons as well as a slightly more detailed version of tex here see the chapter The recent status of leptohadron hypothesis of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy".